随机共振系统输入阈值的频率特性

通过对双稳态系统和Ｈｉｎｄｍａｒｓｈ-Ｒｏｓｅ神经元输入信号阈值的频率特性进行数值计算，分别研究了非自激和可自激随机共振系统输入阈值随信号频率的依赖关系，提出了确定非自激系统阈值的频率特性的解析方法；指出了可自激系统阈值的频率特性可能在某些频区出现反常极小现象，并对产生这一现象的物理原因进行了理论分析． 关键词：     

级联双稳Duffing系统的随机共振研究

研究了级联双稳Duffing系统的随机共振特性, 证明级联双稳Duffing系统变尺度系数、阻尼比和级数等参数的适当调节, 不仅可实现大参数信号的级联随机共振, 而且可优化单级双稳Duffing系统的随机共振特征, 即参数调节的级联双稳Duffing系统能实现比单级双稳Duffing系统更好的随机共振输出. 此外, 级联双稳Duffing系统对方波信号具有良好的滤波整形作用, 可用于实现含噪方波信号的波形恢复. 关键词： 级联双稳Duffing系统 随机共振 变尺度 参数调节     

Aspects of stochastic resonance in Josephson junction,bimodal maps and coupled map lattice

We present the results of extensive numerical studies on stochastic resonance and its characteristic features in three model systems, namely, a model for Josephson tunnel junctions, the bistable cubic map and a coupled map lattice formed by coupling the cubic maps. Some interesting features regarding the mechanism including multisignal amplification and spatial stochastic resonance are shown.     

A new method for weak fault feature extraction based on piecewise mixed stochastic resonance

In a continuous bistable system, when the input signal is continuously increased, the output signal tends to be stable and no longer increases. At this time, the weak signal under strong background noise is difficult to be extracted, which means saturation occurs. Aiming at the saturation characteristics of stochastic resonance (SR), the proposed piecewise nonlinear bistable system (PNBSR) model has achieved certain results. However, the potential barrier in the middle of the PNBSR method still completely uses the potential function of classical bistable stochastic resonance (CBSR). There is no fundamental solution to the fourth-order limitation. This paper explores an improved piecewise mixed stochastic resonance (PMSR) potential model. The fourth-order potential function that restricts particle motion in CBSR is improved to a piecewise second-order potential function. This potential function subverts the shape of the traditional potential function and presents a symmetrical double-hook shape. Based on PMSR model, this paper uses particle swarm optimization (PSO) to select system parameters and elaborates the characteristics of the potential function curve in detail. Under the same conditions, the output signal-to-noise ratio (SNR) curve of the improved system is generally higher than that of the CBSR and PNBSR systems. Experiments on bearings and gears show that the proposed method can accurately extract weak fault features, and the effect is better than the PNBSR method.     

Stochastic resonance in chaotic systems

The phenomenon of stochastic resonance (SR) is investigated for chaotic systems perturbed by white noise and a harmonic force. The bistable discrete map and the Lorenz system are considered as models. It is shown that SR in chaotic systems can be realized via both parameter variation (in the absence of noise) and by variation of the noise intensity with fixed values of the other parameters.     

非对称双稳耦合网络系统的尺度随机共振研究

研究了不同周期信号调制下非对称双稳耦合网络系统的尺度随机共振问题. 针对该网络系统, 首先运用高斯近似和役使原理对其进行了降维, 推导了其简化模型. 在绝热近似条件下, 利用Fokker-Planck方程分别得到了余弦信号和矩形信号调制下信噪比的解析表达式. 在此基础上, 研究了系统的尺度随机共振行为, 并讨论了非对称性、噪声强度、周期信号的振幅和耦合系数对系统尺度随机共振的影响. 结果表明, 两种情形下信噪比均是系统尺度的非单调函数, 说明在此网络系统中产生了共振现象. 关键词： 尺度随机共振 非对称双稳耦合网络系统 余弦信号 矩形信号     

线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振     

大参数周期信号随机共振解析

通过调节双稳系统参数实现大参数频率范围内周期信号的随机共振, 在工程上具有重要意义. 推导了双稳系统参数的归一化变换, 利用归一化变换原理对大参数周期信号的随机共振进行了数值仿真, 阐明该原理适用于任意频率周期信号. 对大参数随机共振用电路模拟进行了实验验证, 揭示了通过调节双稳系统参数可以实现大参数频率范围内的随机共振. 分析了二次采样实现大参数周期信号随机共振的机理, 通过数值仿真与参数归一化变换方法进行了比较. 仿真结果表明, 在输入信号幅度变化的情况下, 二次采样方法易出现发散现象, 而归一化变换具有更好的稳定性与适应性.     

Stochastic resonance on paced genetic regulatory small-world networks: effects of asymmetric potentials

We study the phenomenon of stochastic resonance on small-world networks consisting of bistable genetic regulatory units, whereby the external subthreshold periodic forcing is introduced as a pacemaker trying to impose its rhythm on the whole network through the single unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network remains forever trapped in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker driven stochastic resonance depends significantly on the asymmetry of the two potential wells characterizing the bistable dynamics, which can be tuned via a single system parameter. In particular, we show that the ratio between the clustering coefficient and the characteristic path length is a suitable quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm, but only if the asymmetry between the potentials is practically negligible. In case of substantially asymmetric potentials the impact of the small-world topology is less profound and cannot warrant an enhancement of stochastic resonance by units that are located far from the pacemaker.     

Control of stochastic resonance in bistable system by using periodic signal

<正>According to the characteristic structure of double wells in bistable systems,this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal.Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization.By adding a bistable system with a controllable periodic signal,fluctuations in the single potential well can be effectively controlled,thus affecting the probability transitions between the two potential wells.In this way,an effective control can be achieved which allows one to either enhance or realize stochastic resonance.     

Chaos and reverse transitions in stochastic resonance

Stochastic resonance is a phenomenon that a weak signal can be amplified and optimized by the assistance of noise in bistable system. There is still not enough research on the mutual interplay among system, noise and signal. In this paper, we study the role of every parameter in nonlinear transfer and discover chaos phenomenon in stochastic resonance. To measure the influence of chaos, a trajectory decision function was proposed. Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance.     

双稳系统随机共振的反馈控制

将双稳系统的输出反馈到输入端再作用于系统,提出了采用反馈来控制随机共振的方法.以典型双稳系统为对象,并以信噪比和功率谱放大率作为度量随机共振效应的可观察变量,分别研究了采用线性或非线性反馈函数所产生的随机共振现象.理论分析和数值仿真结果表明随机共振是可控制的.该方法特别适用于系统参数固定或难以改变的系统. 关键词： 双稳系统 随机共振 反馈控制 共振效应     

双稳系统演化的时间尺度与随机共振的加强

噪声作用下的双稳系统存在着单一势阱内的随机波动和两势阱之间的概率跃迁,这两种不同层级的运动具有不同的时间尺度,且低层级的势阱内的波动影响着高层级的势阱间的跃迁．当外作用周期信号的时间尺度与噪声诱导的势阱间概率跃迁达到随机同步时,则能产生随机共振;给系统再加第二驱动周期信号,使其时间尺度与低层级的势阱内的波动相匹配,则存在着频率吸收现象,并能增强双稳系统的随机共振效应． 关键词： 随机共振 双稳系统 层级 时间尺度     

Stochastic resonance and antiresonance in monostable systems

We study characteristics of the output signal in a nonlinear monostable inertial dynamical system with the harmonic signal and Gaussian white noise supplied additively to the input. Several types of monostable systems are examined, and analytical expressions for the output-signal power amplification and signal-to-noise ratio are obtained for such systems for the first time. The main attention is paid to the stochastic resonance and antiresonance phenomena, which manifest themselves as nonmonotonic dependences of the mentioned characteristics on the input-noise intensity. In particular, it is shown for the first time that the output signal-to-noise ratio may have a maximum as a function of the input-noise intensity in a monostable system. This corresponds to the classical definition of stochastic resonance, which earlier was only observed in bistable (multistable) systems. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 899–913, October 2008.     

双稳随机动力系统信号调制噪声效应的数值分析

用数值方法研究了双稳随机动力系统的信号调制噪声效应.结果表明，正弦信号在系统输出中的效应仍为正弦信号，白噪声的效应则为维纳过程，通过选择合适的系统参数，可以减小系统输出中信号和噪声之间的耦合效应，系统可以大大抑制噪声，从而在双稳系统中可以产生信号调制噪声效应. 关键词： 双稳系统 信号调制噪声效应 随机共振     

双稳调参高频共振机理

针对双稳系统的高频信号响应,探讨了双稳调参的高频共振机理.研究表明,二次采样频率变换并不改变双稳结构直接在原系统结构上在与高频映射对应的低频处实现共振,而双稳系统参数调节是调参改变双稳结构并直接在高频处实现共振.双稳系统参数调节之所以能够实现高频随机共振,是因为同时调节双稳系统两参数可使Kramers逃逸速率不存在极限值,突破了随机共振信号频率必须在小频率范围内的限制. 关键词： 双稳系统 高频共振 二次采样频率变换 系统参数调节     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

四稳系统的双重随机共振特性

提出了一类8次势函数并讨论了其分岔特性,得到由左、右2个小尺度双稳势和中间势垒构成的对称四稳系统.建立了在周期力和随机力共同作用下四稳系统输出响应的近似解析表达式,并从能量角度引入功这一过程量来刻画大、小不同尺度双稳势之间的作功能力,发现四稳势中存在着双重随机共振现象.理论分析与数值仿真结果表明,当中间势垒高度大于左右2个小尺度双稳势的势垒高度时,四稳系统的响应随着噪声强度的变化由束缚在小尺度双稳系统中做小幅振动转变为跨越中间势垒的大幅振动,功随噪声强度的变化出现了双峰曲线,存在着双重随机共振,且小尺度随机共振能增强大尺度随机共振的效应.     

State observer for stochastic resonance in bistable system

We investigate numerically stochastic resonance variation in bistable system. Putting signals with different intensities into a bistable system, or adjusting system structural parameters for an input, will produce different motion trajectories. These trajectories contain both chaos and non-chaos parts. We classify these states according to the state of resonance and chaos, and propose a state observer. In this way, bistable system becomes an observable nonlinear system. State observer can provide us with a new perspective that is not available through conventional observation methods. These investigations contribute to nonlinear system optimization, and can also be applied to other interesting noise-induced phenomena.     

具有时滞反馈的非对称双稳系统中的振动共振研究

研究了具有时滞反馈的非对称双稳系统中的振动共振现象. 在绝热近似条件下, 应用快慢变量分离法得到系统响应振幅的解析表达式Q, 分析了时滞参数α和不对称参数r对振动共振现象的影响. 结果表明: 在Q-α平台上, α可以诱导响应幅值的极大值以输入高频信号和低频信号的周期出现. 不对称参数并不影响共振发生的位置, 但是能够增强响应幅值. 在Q-B (B为高频信号振幅)平台上, 共振发生的位置B_VR随着α呈现两种不同的周期关系, 且周期分别为输入高频信号和低频信号的周期. 在Q-Ω (Ω高频信号频率)平台上, 随着时滞参数的增大, 当B较小时, 在Ω的小值区间内, Q呈现出多重共振现象, 在Ω的大值区间, Q趋于定值.